In a large saucepan, saute onion and garlic in butter until tender. Stir in flour until blended. Gradually stir in broth; bring to a boil. Cook and stir for 2 minutes.
Stir in the milk, broccoli, mustard, Worcestershire sauce and nutmeg. Bring to a boil. Reduce heat; simmer, uncovered, for 6-8 minutes or until heated through. Stir in cheese until melted. If desired, serve with additional cheese.